Uploaded February 2025 | Updated September 2026, 1 week ago

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Solving the heat equation

We solve the heat equation, also known as the diffusion equation, ut = D uxx. This models the temperature of an infinite metal rod, and also has applications to Brownian motion. To solve this, we take the Fourier transform on both sides and apply the Fourier miracle, which turns differentiation into multiplication. At this point we are stuck, but what will save us in a future video is the concept of convolution. Get ready for this hot and sizzling adventure through the world of partial differential equations

Link to Part 2: youtu.be/xHOmMhyoptY

Fourier transform playlist: youtube.com/playlist?list=PLJb1qAQIrmmCgatSUjpLQWk1AmeZ0B5MI

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